Trigonometry (10th Edition)

Appendix A - Equations and Inequalities - Page 418: 80

Answer

$[-5,\infty)$

Work Step by Step

Step 1: $-3x-8\leq7$
Step 2: Adding $8$ to both sides, $-3x-8+8\leq7+8$
Step 3: $-3x\leq15$
Step 4: Dividing both sides by -3 (this reverses the direction of the inequality symbol):
$\frac{-3x}{-3} \geq \frac{15}{-3}$
Step 5: $x\geq-5$
According to the inequality, the interval includes $-5$ and all values greater than $-5$. Since $-5$ is part of the interval, a square bracket is used on its side. On the other hand, we represent all values greater than $-5$ by the symbol $\infty$. Therefore, a parenthesis is used on its side.
Therefore, the interval notation for this inequality is written as $[-5,\infty)$.